(i) The difference between two numbers is 26 and one number is three times the other. Find them.
(ii) The larger of two supplementary angles exceeds the smaller by 18 degrees. Find them.
(iii) The coach of a cricket team buys 7 bats and 6 balls for Rs 3800. Later, she buys 3 bats and 5 balls for Rs 1750. Find the cost of each bat and each ball.
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Solution:
i) Let us assume the larger number is x and smaller number is y. Then we have following equations, as per question:
x = y + 26 and x = 3y
Substituting the value of x from second equation in the first equation, we get;
x = y + 26
Or, 3y = y + 26
Or, 2y = 26
Or, y = 13
Substituting the value of y in second equation, we get;
x = 3y
Or, x = 13 x 3 = 39
Hence, x = 39 and y = 13
ii) Let us assume the larger angle is x and smaller angle is y. Then we have following equations;
x = y + 18 and x + y = 180o
Substituting the value of x from first equation in second equation, we get;
x + y = 180o
Or, y + 18 + y = 180o
Or, 2y = 180o - 18o = 162o
Or, y = 81o
Substituting the value of y in first equation, we get;
x = y + 18
Or, x = 81o + 18o = 99o
Hence, x = 99o and y = 81o
iii) Let cost of each bat = Rs x
Cost of each ball = Rs y
Given that coach of a cricket team buys 7 bats and 6 balls for Rs 3800.
So that 7x + 6y = 3800
6y = 3800 – 7x
Divide by 6 we get
y = (3800 – 7x) /6 … (1)
Given that she buys 3 bats and 5 balls for Rs 1750.so that
3x + 5y = 1750
Plug the value of y
3x + 5 ((3800 – 7x) /6) = 1750
Multiply by 6 we get
18 x + 19000 – 35 x = 10500
-17x =10500 - 19000
-17x = -8500
x = - 8500 / - 17
x = 500
Plug this value in equation first we get
y = ( 3800 – 7 * 500) / 6
y = 300/6
y = 50
Hence cost of each bat = Rs 500 and cost of each balls is Rs 50
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